Bifurcation and Accusation

Let's consider this argument:

1. Polly is either a [Cat] or a [Dog]. (Either [A] or [B])
2. Polly is not a [Dog]. (Not [B])
3. Therefore Polly is a [Cat].  (Therefore [A])

This sounds reasonable, right?

But what if Polly is actually a parrot?  In such a case, this argument would be untrue because it fails to consider that other options exist.

I bring this example of logical fallacy up because it seems to be common in today's debate on moral and political issues in an "Either with us or with the enemy" mindset.  If one extreme is not true, the other extreme must be true.

Thus we see homosexual activists label whoever believes homosexual acts are wrong support the "persecution" of homosexuals.  Whoever opposes Pastor Terry Jones in his burning of the Koran must therefore think Islam is as good as Christianity.

Contradictory and Contrary Statements

Such an argument confuses Contradictory statements with Contrary Statements.

A Contrary statement would be: It is Either Hot or Cold.

A Contradictory statement would be: it is either Hot or not Hot.

With contrary statements, there is the possibility of it being neither one or the other – that is — both can be false.  With contradictory statements,  only one can be true, and one must be true.

Denouncing False Accusations

Opposition to a certain belief is not endorsement of the opposite.  Opposition to homosexual acts is not favoring the persecution of homosexuals.  Opposing Pastor Terry Jones is not thinking Islam is equally valid with Christianity.  Opposing Democrats does not mean one supports Republicans.  Opposing remarriage when a prior marriage is seen as valid is not "wanting people to suffer."  The Church not excommunicating a dissenter does not mean supporting the dissent.

See the principle here?

When a person says [Not B], it is wrong to accuse them of supporting  [A].  Saying [Not B] merely means opposition to [B].  Saying such a person supports [A] on these grounds is to put words into their mouth without the right to do so.

Discernment is Necessary

Now of course we need to distinguish between bifurcation and real dilemmas.  Sometimes there are really demonstrably two choices.  Either 2+2 is 4, or 2+2 is 5. 

1. Either 2+2 Is [4] or is [5]. (Either [A] or [B])
2. 2+2 is [4]. ([A])
3. Therefore 2+2 is not [5] (Therefore not [B])

In such a statement, we are not reasoning from what is not to what is.  Rather we are taking what is and excluding what is not.

Likewise, if the Catholic Church teaches that we must believe "Jesus Christ is fully God and fully human" to hold what the Church teaches, anyone who holds that "Jesus is a mere man" is not holding to what the Catholic Church teaches.

1. Either The Catholic Position is [Jesus Christ is fully God and fully human] or [Jesus is a mere man] (Either [A] or [B])
2. The Catholic Position is [Jesus Christ is fully God and fully human] ([A])
3. Therefore [Jesus is a mere man] is not the Catholic position. (Therefore Not [B])

The difference is again, we take what is true [A] and therefore reject [B] since A ≠ B, while Bifurcation argues that [Not B] means [A]

In short, we must discern whether an "Either-Or" situation does accurately limit the situation to two choices where the acceptance of one means the rejection of the other, or whether one claims the denial of one means the acceptance of the other.

• "Either homosexual acts are wrong or they are not wrong" does limit accurately to two possible choices. (Either [A] or [Not A])
• "Either one supports gay marriage or they are homophobic" does NOT accurately limit to two possible choices. (Either [A] or [B]).

The first does accurately divide.  The second does not.

Conclusion

It is important to recognize the fallacy of Bifurcation because it can easily be used to twist things around to either sanctify one's own position or demonize an opponent.  With the recent rhetoric in the media over "gay marriage," over political agendas and other things, we need to be on guard.  The Christian needs to especially be on guard as moral issues under attack will often be used to demonize us based on the claim that because we don't support [B], it must mean we support [A] – even though [A] is also against our beliefs as Christians.